Learning-Based Nonlinear State Estimation With Unknown System Dynamics

Abstract

Accurate system dynamics are often difficult to obtain in practical industrial processes, which limits the applicability of model-based state estimators. This paper proposes a novel learning-based nonlinear state estimation method for systems with an unknown state equation. A stochastic configuration network is trained from offline state trajectories to predict the state increment between two consecutive sampling instants. The one-step prior state is then obtained by adding the learned increment to the previous state estimate. To describe the uncertainty induced by model approximation errors and process disturbances, the prediction covariance is treated as an unknown random matrix and recursively updated together with the state through a variational Bayesian estimation framework. Lorenz-system simulations compare the proposed method with representative learning-based estimators and a known-model extended Kalman filter reference. The results show compact model size, fast online inference, competitive accuracy, and improved robustness under process noise mismatch.